A particle is moving in a straight line.its displacement at time t is given by s (in m) =-4t^2+2t,then its velocity and acceleration at time t=1/2 second are..???

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Answer 1 · 2018-08-07T05:07:17

Please see the explanation below.

The displacement is

$s (t) = - 4 t^{2} + 2 t$ $s(t)=-4t^2+2t$

The velocity is the derivative of the displacement

So,

$v (t) = \frac{d s}{d t} = - 8 t + 2$ $v(t)=(ds)/dt=-8t+2$

And when the time is $t = \frac{1}{2} s$ $t=1/2s$ , the velocity is

$v (\frac{1}{2}) = - 8 \cdot \frac{1}{2} + 2 = - 4 + 2 = 2 m s^{- 1}$ $v(1/2)=-8*1/2+2=-4+2=2ms^-1$

The acceleration is the derivative of the velocity

$a (t) = \frac{d v}{d t} = - 8 m s^{- 2}$ $a(t)=(dv)/dt=-8ms^-2$

The acceleration is constant whaever the value of $t$ $t$